the reacn 2NO+BR2 =2NOBr is supposed to follow followng mech.

1)NO+Br2(fast)=NOBr2 2)NOBr2 +NOBr(slow) =2NOBr.suggest the rate law expressn.

To determine the rate law expression for the reaction 2NO + Br2 → 2NOBr based on the proposed mechanism, we need to analyze each step of the mechanism and how they contribute to the overall reaction rate. The rate law is a mathematical relationship that describes how the rate of a reaction depends on the concentration of its reactants.

Understanding the Mechanism

The mechanism you provided consists of two steps:

• Step 1: NO + Br2 (fast) → NOBr2
• Step 2: NOBr2 + NOBr (slow) → 2NOBr

In this case, the first step is fast, and the second step is slow. The slow step is typically the rate-determining step, meaning it controls the overall rate of the reaction.

Identifying the Rate Law

For the rate law expression, we focus on the concentrations of the reactants involved in the rate-determining step. Since the second step is the slow step, we will use it to derive the rate law.

In the slow step, we have:

• NOBr2 (intermediate)
• NOBr (reactant)

However, we need to express the rate law in terms of the reactants present in the overall reaction. The intermediate NOBr2 is produced in the fast step, and its concentration can be related to the concentration of the reactants in the first step.

Expressing the Concentration of NOBr2

From the first step, we can express the concentration of NOBr2 in terms of the concentrations of NO and Br2:

Since the first step is fast and reaches equilibrium quickly, we can assume that the formation of NOBr2 is proportional to the concentrations of NO and Br2:

NOBr2 = k1[NO][Br2]

Here, k1 is the rate constant for the first step. Now, substituting this expression into the rate law for the slow step gives us:

Final Rate Law Expression

The rate of the slow step can be expressed as:

Rate = k2[NOBr2][NOBr]

Substituting the expression for NOBr2, we get:

Rate = k2(k1[NO][Br2])[NOBr]

To simplify, we can combine the constants:

Rate = k[NO][Br2][NOBr]

Where k = k1 * k2 is the overall rate constant for the reaction. This expression indicates that the rate of the reaction depends on the concentrations of NO, Br2, and NOBr.

Summary of the Rate Law

In summary, based on the provided mechanism, the rate law for the reaction 2NO + Br2 → 2NOBr is:

Rate = k[NO][Br2][NOBr]

This expression captures the relationship between the rate of the reaction and the concentrations of the reactants involved in the rate-determining step. Understanding these relationships is crucial for predicting how changes in concentration will affect the reaction rate.